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Getting Started: Establishing Routines & Procedures During the 1st 20 Days of Math
Oerie!: For students, a successful experience with math begins with the basics: how to think like an active mathematician, how to speak mathematically, and
how to record and share their thinking. This guide is intended for grades 3- but can be used for !-" with modifications, and may be extended, condensed, or
modified according to students# needs.
$s you prepare to implement the % st "& 'ays of (ath during the )& minutes of math instruction, keep in mind that it will be necessary to be flexible. These -%
minute mini lessons are to be incorporated into the daily lesson. *rade level teams may meet periodically to monitor and ad+ust progress. lear statements and
clear demonstrations of roles and procedures need to be established. $ll points and aspects need to be repeated, charts or artifacts of support are to be posted and
referred to again and again.
Goals: The goals of implementing the instructional strategies included in this document are to
• help students think of themselves as mathematicians who en+oy and actively participate in math
• establish consistent classroom roles, rituals, routines and procedures that support teaching and learning
• increase rigor by having students explore, express, and better understand mathematical content though process skills communication, connections, reasoning
and proof, representations, and problem solving/.
"ac#ground: 0ased on the idea of The First "& days of 1ndependent 2eading by Fountas 4innell, these lessons have been developed to establish the roles,
rituals, routines and procedures needed for effective mathematics instruction.
Princi$les of %earning are the foundation of this document. $ll students are told that they are already competent learners and are able to become even better
through their persistent use of strategies and by reflecting on their efforts. riteria for 5uality and work are explicit, accessible to all students, displayed publicly,
and change over time to respond to level of rigor as learning deepens.
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Outco(es
)rtifacts Resources *eacher +otes
Day 1 Manage(ent:
6stablish 2outines and
2outines for
1ndependent and7or
ooperative (ath
*roups
4rinciples of 8earning:
lear 6xpectations
6stablish
student
expectations
during
(athematics
instruction.
'iscuss the
importance of
9$rtifacts such
as criteria7element
charts, student
work criteria7elements
and
instructional
aides7manipulatives
;tudents understand
and learn that
information will be
posted around the
classroom for them
to use to make their
work better, to
support their
learning and to help
them review
concepts as they are
learned.
;tudents identify
criteria to create a
9*ood <ork chart
to post.
4ost 9(eets <ork process
chart to which
students can refer. $
mneets work chart should
have less than = criteria to
be effective./
6xample:
• ;tay on Task
• ;peak7write
mathematically7accountabl
e talk
• 0e an active listener and
participant.
• 2espect and organi>e
math materials7manage
tools
hart 4aper
(arkers Topics to address:
$ccountable Talk
(anaging Tools
Time on Task
?oise 8evel
reate $rtifact of skills
they have brought from
last years learning.
Day 2 Manage(ent:
@ow and why do
mathematicians use
toolsA
(athematicians
use math tools
to help solve
problems.
'iscuss
mathematical
tools and howthey are to be
used and
stored.
;tudents become
familiar with the
math tools in the
classroom.
$dd notes to the 9(eets
<ork artifact about
placing materials in their
proper storage
containers and location
after use.
'evelop the
oncept that
students use
manipulatives.
This is a good
time to establish
reinforce the9how and why
of using
mathematical
tools.
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)rtifacts Resources *eacher +otes
Day , Proble( Soling:
(athematicians solve problems using a process.
There is a
process
involved whensolving
problems.
;tudents understand
the importance of
problem solvingevery day.
;tudents will learn
that there is a
process involved
when solving
problems.
'evelop and post a
process chart of the
mathematician#s,4roblem
;olving (odel.The four steps are:
• Bnderstand the
problem,
• 'evise a plan,
• arry out the plan, and
• 8ook back.
There are many record
keeping pneumonic
devices that follow this
model. The selectionof one to use school
wide is most effective
4roblem ;olving (odel
hart paper
6ach day
students will
engage in problem solving
during their math
block -or# ti(e
and.or
Proble(
of the Day
4ost the chart on
the wall in
student- friendly
standard language.
Day /
-riting.Re$resentations
in Math
(athematicians write
about their thinking as a
way to process
information
2epresentation is a
4rocess ;kill.
(athematicians
use and record
mathematical
representations
to interpret and
model
everyday life
activities.
1ntroduce
1nteractive
(ath Cournals.
;tudents understand
that they are
expected to write
about their
mathematical
thinking on a daily
basis.
;tudents understand
that writing about
their thinking is a
way to represent
mathematical
concepts.
;tudents understand
that the +ournal is a
mathematical tool. ie.
4ersonal
artifact7resource7+ournal
Dn a chart, post a model
of the left and right
side of math interactive
+ournal
4ost the mini lesson
concept
7standard7essential
5uestion
;tudent +ournal
(odel of +ournal
;entence strip for
6ssential
Bnderstanding Euestion
$t the end of the
lesson, use the
(ini lesson
standard essential
uestion as a
+ournal prompt.
@ave students
write about their
understanding.
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)rtifacts Resources *eacher +otes
Day Mathe(atics is a
%anguage:
1n a math classroom,speciali>ed
language is
used.
1ntroduce word
wall
;tudents understandthat we use
speciali>ed terms to
define mathematical
concepts.
;tudents use
mathematical terms
to build conceptual
knowledge.
1llustrated ocabularywords
Cournal
$s you introduce newvocabulary,
make sure that
students record
these words/ in
their +ournal.
@ave students
write their
definition of
vocabulary
words/ and
make a real life
connection intheir +ournal.
Day 3
'o((unication is
a $rocess s#ill
4rinciples of 8earning:
9$ccountable Talk
(athematicians
communicate
about their
work orally and
make
con+ectures
about their
findings.
;tudents understand
that communication
is a process skill
that helps develop
rigor.
4ost and discuss 9$ccountable
Talk
to encourage students to speak
mathematically and to speak in
complete
thoughts
Think about what
strategies you will use
for calling on each
student daily.
$dd communication
criteria to 9(eets
<ork chart if needed
;tudents must
develop the
habit of
speaking in
complete
thoughts when
communicating
orally.
Bsing the language of
the standards
encouragesstudents to
communicate
about their
thinking
throughout the
lesson.
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)rtifacts Resources *eacher +otes
Day 4 'ollaboration
4rinciples of
8earning:
;ociali>ing
1ntelligence
.
(athematicianswork
collaboratively,
developing
good work
ethics and
maintaining a
sense of
responsibility.
;tudents learn thatthey can work with
others to share
information and to
learn new
information.
6stablish rules forworking in groups or
enters
PARTNER WORKING
STANDARDS ARRAYS TASK
#1 ROLL DICE FOR FACTORS
#2 BUILD ARRAY USINGTILES
#3 DEFEND MODEL WIT GRID PAPER
!USE AT LEAST 2
OPERATIONS TO PRO"E!
BONUSTRY OTEROPERATIONS
4ost rules and directions for
center work
(ake sure toestablish rules
and clear
directions so
that independent
group work will
be successful.
$fter
establishing
rules, have the
students practice
during -or# *i(e
Day 5 6ustification
2easoning and 4roof
is a process skill.
9losing
(athematicians
+ustify their
thinking
The teacher
students pressfor accurate
and appropriate
evidence of
their claims,
including
references to
the strategies,
manipulatives or prior
classroom
experiences.7work time
;tudents understand
that when they
+ustify their
thinking they
deepen their
understanding of aconcept.
;how
models7examples of
5uality work such
as +ournal entry,
student work products.
etcthat reinforce students#
+ustification of their
thinking.
Custify means:
• explain
• describe
• prove
• give reasons
• show you understand
4ictures, numbers, words
'uring math
instruction,
make sure that
students are
explaining
thoughts incomplete
sentences $%e&
spe'()&* '&+
$r),)&* . This
practice will
reinforce and
develop the skill
of reasoning and
proof.
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Day 7 )ccountability
4rinciples of 8earning:
;ociali>ing 1ntelligence
;elf (anagement of
8earning
(athematiciansare accountable
for the learning
tasks.
lassroom
practice holds
all students
accountable for
using learning,
problem
solving, and
helpingstrategies.
;tudents understandthat they share in
the responsibility
for their own
learning
6mphasi>e that the9$rtifacts in
the classroom are there
as referents to help
make their work better
$dd accountability to classrules.
!eep remindingthe students that
the referents on
the wall and
+ournals are
mathematical
tools for their
use.
Day 10
Re$resentation
2epresentation is a
process skill.
(athematician
use multiple
ways to
represent ideas
;tudents understand
that in math there
are multiple ways to
represent
mathematical ideas.
reate a chart and
explain that students
can
represent math
concepts using
pictures,
words, numbers,
symbols, manipulatives
and
in relevant situations.
'iscuss how
students can
represent
concepts using
manipulatives,
pictures, numbers and
words etcG
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Day 11 'onnections
onnections is a
process
skill.
(athematicians
wonder how
math connects
and relates to
the world
around them.
(athematicians
make
connections
between
mathematicalconcepts
;tudents know they
can relate math to
the world around
them, inside and
outside of the
classroom.
;tudents also
understand that
mathematical ideas
can be interrelated.
;elf to <orld
connections shared.
(easurementHcooking
(oneyH+obs
TimeHappointments
6stimationHshopping
(ultiplicationHbuilding
These
connections can
also be made
when
transitioning to new
Bnits of instruction.
(odel how concepts
are building and
interrelated
Day 12
Self Monitor
4rinciple of
8earning:
lear 6xpectations
;elf
(anagement of
8earning
9losing
(athematicians
modify and
ad+ust their
work as needed.
;tudents revise
their work to meet
5uality criteria on a
systematic basis as
appropriate.
1ntroduce an element chart and7or
rubric for self monitoring
of work.
4ost 2ubric and7or
6lement artifact for
4roblem ;olving7task
Through
discussion,
develop a clear
understanding
of criteria and
how work will
be scored.
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Day 1,
Proble( Soling
4rinciples of
8earning:
$cademic 2igor in a
Thinking urriculum
(athematicians
solve problems
using a variety
of strategies.
;tudents are
expected to
engage in high
thinking
demand by
raising
5uestions,
problemsolving, and
reasoning.
;tudents share and
recogni>e multiple
strategies used to
solve a problem
-or# ti(e and.or
Proble( of the
Day
0uild or add to a
strategy wall showing
student created
models of strategies.
(ake
connections
between
strategies.
Day 1/
Math Strategies
4rinciples of
8earning:
lear 6xpectations,
;ociali>ing
1ntelligence,
;elf (anagement of
8earning,
$cademic 2igor in aThinking urriculum
(athematicians
choose from
many strategies
to solve
problems.
;tudents understand
they have a handy
source for strategies
to help them solve
problems
1ntroduce Proble(
Soling )rtifact
6xplain that
the 4roblem ;olving
artifact has examples
and pictures of many
different kinds of
strategies to help
students with problem
solving. ;tudents can
refer to their +ournal.
$dd additional strategies to
;trategy
<all.
During -or# *i(e
teacher
facilitates as
students skim
the problem solving
artifact to
select a strategy
to help them
solve the problem.
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)rtifacts Resources *eacher +otes
Day 1 Math
Strategies
4rinciples of 8earning:
lear 6xpectations,
;ociali>ing 1ntelligence,
;elf (anagement of
8earning,
$cademic 2igor in a
Thinking urriculum
(athematicians
organi>e their
work in
different ways.
;tudents will
understand how to
utili>e a recording
sheet or guide.
1nclude recording tools
in math +ournal for
student reference.
Test taking strategies,
writing frames, sentence
starters
1ntroduce a
4roblem
;olving
2ecording ;heet
as a student tool
Day 13 8ocabulary
Deelo$(ent
4rinciples of 8earning:
;ociali>ing 1ntelligence
(athematicians
use a variety of
strategies to
build
vocabulary
;tudents will
practice using
different tools to
strengthen their
math vocabulary.
;tudents
consistently use the
academic language
specific to thediscipline being
studied.
;elect models/
implement with students
Frayer, $0, cards,
+ournal etc/.
1ntroduce
strategies one at
a time across
multiple days of
instruction.
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)rtifacts Resources *eacher +otes
Day 17 Guided Math 2eview all elements
of standards basedclassroom
Teachers and students
practice gradual release
of control
1ndependently used by
students during both
work time and closing.
omplete collection of
data per groups
Day 20 Guided Math ;tudents and teacher practice all elements of
2ituals and 2outines to
complete ulminating
Task from Bnit %
Teachers and students practice gradual release
of control